The language of models

Lecture 15

Dr. Mine Çetinkaya-Rundel

Duke University
STA 199 - Fall 2022

October 20, 2022

Warm up

While you wait for class to begin…

Clone your ae-12 project from GitHub, render your document, update your name, and commit and push.

Announcements

Project proposals due Friday

Goals

What is a model?
Why do we model?
What is correlation?

Setup

library(tidyverse)
library(gt)

Modelling

Modelling cars

What is the relationship between cars’ weights and their mileage?
What is your best guess for a car’s MPG that weighs 5000 pounds?

ggplot(mtcars, aes(x = wt, y = mpg)) +
  geom_point() +
  labs(
    x = "Weight (1000 lbs)",
    y = "Miles per gallon (MPG)",
    title = "MPG vs. weights of cars"
  )

Modelling

Use models to explain the relationship between variables and to make predictions
For now we will focus on linear models (but there are many many other types of models too!)

Modelling vocabulary

Predictor (explanatory variable)
Outcome (response variable)
Regression line
- Slope
- Intercept
Correlation

Predictor (explanatory variable)

base <- ggplot(mtcars, aes(x = wt, y = mpg)) +
  geom_point() +
  labs(
    x = "Weight (1000 lbs)",
    y = "Miles per gallon (MPG)",
    title = "MPG vs. weights of cars"
  )

mpg	wt
21	2.62
21	2.875
22.8	2.32
21.4	3.215
18.7	3.44
18.1	3.46
...	...

Outcome (response variable)

mpg	wt
21	2.62
21	2.875
22.8	2.32
21.4	3.215
18.7	3.44
18.1	3.46
...	...

Regression line

Regression line: slope

Regression line: intercept

Correlation

Ranges between -1 and 1.
Same sign as the slope.

Visualizing the model

ggplot(mtcars, aes(x = wt, y = mpg)) +
  geom_point() +
  geom_smooth(method = "lm")

Application exercise

`ae-12`

Go to the course GitHub org and find your ae-12 (repo name will be suffixed with your GitHub name).
Clone the repo in your container, open the Quarto document in the repo, and follow along and complete the exercises.
Render, commit, and push your edits by the AE deadline – 3 days from today.